MinT - Best Known (221−107, 221, s)-Nets in Base 4

Best Known (221−107, 221, s)-Nets in Base 4

(221−107, 221, 130)-Net over F₄ — Constructive and digital

Digital (114, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(221−107, 221, 174)-Net over F₄ — Digital

Digital (114, 221, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−107, 221, 2123)-Net in Base 4 — Upper bound on s

There is no (114, 221, 2124)-net in base 4, because

1 times m-reduction [i] would yield (114, 220, 2124)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 887813 081471 332275 486526 662856 574268 827956 374573 486935 866898 823171 068046 068310 629772 573114 556983 824448 344348 449708 100032 472329 663352 > 4²²⁰ [i]